High-frequency impedance transformer for transmission lines



gral multiples thereof so as to convert the pure resistance afforded bythe transformer in accordance with the invention to some other desiredvalue.

In order that the invention may be clearly understood and readilycarried into effect it will now be more fully described with referenceto the accompanying drawings, in which:

Figure l illustrates diagrammatically a transformer in accordance withone form of the invention,

Figures 2 and 3 illustrate diagrammatically transformers in accordancewith the form f thev invention shown in Figure -l associated withfurther sections of transmission line for converting the pure resistanceto a desired value,

Figure 4 illustrates the application of the invention to the coupling ofaA coaxial line circuit to awave guide, Y

Figure 5 illustrates diagrammatically the coupling of two waveguides bya coaxial line circuit,

Figure 6 illustrates diagrammatically an impedance transformercomprising a section of waveguide, and

Figure '7 illustrates diagrammatically a modication of the arrangementshown in Figure 6.

Referring now to Figure l of the drawings which illustrates theinvention as applied to a transformer comprising a section of coaxialline,

the reference numeral. 8 indicates a section of coaxial line feeding acomplex impedance A-l-gB indicated by the reference numeral 9. In orderto make the complex:impedance appear to be a substantially non-reactiveor pure resistance at the end of the transmission line 8 an impedancetransformer is inserted between the line 8 and the impedance 9 indicatedat I0 composed of a further section of coaxial transmission line thelength and the characteristic impedance Zo of the section I0 and thecomplex impedance 9 are so related to one another that .of the compleximpedance; Where the length of the section I0 is equal to n oddeighth-wavelengths then when 'n is l, 5, 9 etc., the value of the pureresistance is given by the expression and when n is 3, 7, ll etc., thevalue of the pure resistance is given by the expression M-B M M+B whereM is the modulus of the complex impedance. Y j Y If the valueof thesubstantially pure resistance afforded by the transformer is not of therequired value, then it is possible to employ, in conjunction with thetransformer, a further section of a transmission line effectively equalto one-quarter of a wavelength or odd integral multiples thereof so asto convert the pure resistance afforded by the transformer in accordancewith theiinvention to some other4 desired value. u. Figure 2 'ofk thedrawings illustrates the introduction of such a quarter wavelengthsection Il between the section I0 and vthe complex impedance 9, whilstFigure 3 of the drawings illustrates the introduction of the quarterWavelength section II between the line 8 and the section I0. In thelatter case, assuming that the complex impedance A-i-y'B is transformedby the transformer I9 to a pure resistance R and it is desired toconvert the pure resistance R to another pure resistance R', forexample, in order to provide an impedance match with the line 8, thenthe characteristic impedance Zo of the 'quarter wavelength section II isgiven by Whilst the invention is capable of a wide variety of uses, itis of particular importance in matching a coaxial cable to a wave guide.Heretofore when it has been desired to effect an impedance match betweena cable and a waveguide, such has been accomplished by connecting thecoaxial cable to a probe projecting into the waveguide. To effect animpedance match two requirernents have-to be satisfied. Firstly, theresistive component of the guide impedance as seen from the end of the4coaxial cable must be made equal to the characteristic impedance of thecable, and, secondly, the reactive component of the guide impedance asseen from the end of the coaxial circuit must be made zero. Usually, inorder to satisfy these requirements the length of the portion of theprobe which projects into the guide is adjusted so that the resistivecomponent is of the required value which usually leaves a large reactiveterm which is then tuned out by varying the position of a tuning pistonassociated with the waveguide. It has been found that it is evensometimes necessaryrto employ additional tuning plungers. On accountofthe number of adjustable elements that it isrnecessaryrto employ insuch an arrangement the latter is not only complicated to adjust but theimpedance match is liable to be disturbed 4by mechanical shock.Furthermore, the matching of a cable to a, waveguide in this mannernecessitates an accurate balance tok be made between two relativelylarge reactances and hence any small change, in the operative wavelengthwhich changes either or both'of the two opposing reactan'ces usuallyresults in the two reactances becoming unequal giving rise to arelatively large residual freaGtance. Thus the arrangement describedaffords only a satisfactory impedance match over a relatively narrowfrequency band.

Figure 4 of the drawings illustrates the invention as employed to obtainan impedance match between a coaxial cable I2 and a waveguide I3. Oneend of the waveguide I3 is closed by a conductor I4 which may bepermanently fixed in position as distinct from the adjustable pistonemployed in the prior arrangement above referred to and the coaxialcable is connected toa probe I5 projecting into the waveguide, theprobel also being rigidly fixed in position in any suitable manner anddisposed at a desired position with reference to the closed endof theguide. The probe I5 'may comprise a projecting portion of ens-ancona thecentre@ conductor of the, coaxial cablefthe; outer vconductor' of whichvis connected to` the" waveguide, as shown. Thel impedance at the: pointwhere the probe passes intothe waveguide vdetermined by any of the wellknown means and"T in general, this impedance will be complex not equalto the characteristic impedancelof the coaxial cable. In order tolconvert the com-.- plex impedance into` a substantially pure resistancea transformer in accordancewith the invention is employed which, asshown, comprises a sleeve I6 surrounding the probe I5 or centreconductor and insulated therefrom, said sleeve being-preferablyone-eighthof a wavelength'long. The characteristic impedance of thetransmission line formed by the sleeve I6 and the portion of the probel5 or centre conductor surrounded thereby is made equal to the modulusof the complex impedance. This transformer wi1lj convert the compleximpedance to a pure resistance Rand: if it isf necessary to convert thepure resistance R.' t'o aI value equal to the characteristic impedanceof the-coaxial cable in order properly to terminate the'coaxial cable,then a further transformer effectively equal in length to one-quarter ofa wavelength is then inserted between the cable -l3 and-the -transformerin accordance with the invention, the characteristic impedance of theqnarter-wave transformer being made equal rto whereZo is thecharacteristicimpedance of the coaxial cable.v The quarter-wavetransformer, as shown, comprises a sleeve I1 surrounding yand insulatedYfrom the centre conductor of the coaxial cable and it may be convenientin practice to form the sleeves I6 and' Il integrally with one another,the sleeves iitting within-.and being connected to the outer conductorof the cable, as shown. The construction described will provide animpedance match between a coaxial cable and a waveguide which is of arigid nature and -requires no adjustment after being initially correctlyassembled. If desired the space between the centre conductor and saidsleeve may be lle'd'with solid insulation and it'will thereforebeappreciated that the physical lengths of the vtransformers may bedifferent from their electrical lengths depending upon the dielectricconstant oij'the insulation employed.

"It will be appreciated from the abovethatan impedance match can beobtained whatever is the length of the portion of the probe l5 Whichprojects into the waveguide and furthermore, the

match can be obtained whatever the position of' the probe relatively tothe closed end of the wave.- guide. This is advantageous since it ispossible thereby to make the arrangement less susceptible to' changes ofoperating frequency. As stated above, the magnitude of the compleximpedance as seen through the transformer according to the inventionwhen employing a transformer effectively 4equal to one-eighth of awavelength long, is equal to M +B Mv 'FB and if B is small compared withA, that is to say, about one-fifth or less, the expression reducesapproximately to A+B. Hence, if the length of the probe is adjustedtogether with the position ofithe closed end of the guide so thatthewaveguide'impedance has its two components A and B varying withfrequency in such a wayv that the Stunfoffthe twois constant, thenvtheimpedance quencies in such a wayv that 4the* sum of'thetwo'componentsfis constant'. Hence, such anarrange-- ment will afford animpedance'inatch over arelfa tively'wide frequency range.

If desired, two` sections of waveguide may beV connected together by alength of coaxial' cableeach end of`which is matched to itsassociated?waveguide by thev construction describedk with reference Ato Figure 4.Figure 5 illustrates such an arrangement, the reference Ynumerals I1Vand L8 indicati-ng two sections of waveguide andltlie numeral I 9 alength lof coaxial cable. The coaxial cable `is provided with arotatable joint 2G, such as the plug and socket joint described in thespecification of British patent application No. y11,862/42, theprovision of such a joint eri--V abling the two sections of waveguide tobe rotated with respect to one another without the necessity ofproviding specially constructed joints in the waveguideA sections.Heretofore, when it has been desired to employ two sections of waveguideVmounted 'for relative rotational movement' it has been usuallynecessary to provide special tuning plungers and to,maintain thedistance between the two waveguide sections very small and of a fixeddimension. If the two sections of waveguide are coupled by meansr of 'a'coaxial cable as shown in Figure 5, the distance'betweenr the twowaveguide sections can bemade ofv any desired length, since the couplingis afforded' by a coaxial cable which can be of any appropriate lengthwithout disturbing the impedance match. There vis also an addedadvantage that" the coaxial cable joiningthe two waveguides can be bentso as to negotiate corners or other obstructions. The dimensions of thecoaxial cable should be chosen to afford a minimum losse but thedimensions must not besuch as to---permitV the propagation of unwantedmodes.

The-invention can also' be appliedto` impedancetransformers lcomposedAoi" sections of waveguide.

It is known that thegtheory of two-wire transmission lines, such ascoaxial cables, can be applied to waveguides providing that inve-anygiven problem the guides have substantially the same physical dimensionsand energy of the same mode is Vvtransmitted through'the guides; In thecase of a two-wire transmission line the impedance at' any pointisdefined as the ratio of voltage to the current at that point. In thecase'of a waveguide, however, vthe impedance at any point is dened asther ratio of the-transverse electric field'to the transverse magneticfield at that point.

`Suppose that irl-any guide `of `any form in crosssection there arethree axes, 5c, y and a mutually at right-angles and that z is the axisalong which propagation occurs, thenpthe `z :aharacteristic gimeupedance Zo ofthe, guide is o, n Hr 'Hz these two ratios having the samevalue. ratio gives -the'samevalue at everypoint in the guide but isdiiferent for each mode lof lthe energy transmitted.

VvFor waves (or transverse electric waves) the ratioibecomes M/Ao, whereMis thewavelength in air and M is the corresponding value in the guide.VFor E waves (or transverse magnetic waves) the ratio is where k is thedielectric constant of the material in the guide and the permeability ofthis material is assumed to be unity. Since M depends on the particularE or H mode being transmitted land lalso on the dimensions of the guide,it follows that the characteristic impedance of the guide is also afunction of these quantities. In practice, however, energy of only onemode is propagated and since, as stated above, the two-wire theory onlyapplies to waveguides when the physical dimensions of the latter rem-ainsubstantially constant, the problem of applying the present invention towaveguides is considerably simplied.

The guide most commonly employed is one of rectangular cross-section andin such a guide energy of the Rio mode is usually employed. With such -aform of guide and energy of the stated mode, the characteristicimpedance of the guide is where a is the longer side of thecross-section of the guide. The ratio Ag 2a guide 2l feeding a hollowresonant cavity 22 ,5

which presents to the waveguide a complex impedance A-l-y'B. In order toconvert the complex impedance into a substantially pure resistance awaveguide transformer 23 composed of a section of waveguide is insertedbetween the waveguide 2l and the cavity 22, the length and thecharacteristic impedance Zo of the section 23 and the complex impedance22 being related to one another in accordance with Formula 1 heretoforereferred to. The desired characteristic impedance of the section '23 isimparted by providing the section 23 with a suitable dielectric mediumindicated at 24. Preferably, as in the transformer shown in Figure l,the length of the section 23 is equal to one-eighth of the operatingwavelength, in which case the impedance Zo of the section 23 is madeequal to the lmodulus of the complex impedance.

Theoretically, the desired impedance of the waveguide section can beattained by suitably choosing the dielectric medium within the guidesection, but in practice, however, any material which is sufficientlyloss free to be used in a guide has substantially unit permeability withthe result that a complication may arise due to the fact that whereas adielectric constant of unity is obtainable by using air and dielectricconstants from about 2.5 to 100 can be obtained by using,

for example, polystyrene suitably loaded with titanium dioxide, there isno available suitable substance which affords a constant between unityand 2.5. If therefore any given problem requires a dielectric constantwithin the range of 1 to 2.5 or between zero and unity, the difculty canbe overcome by employing two sections in series with dielectrics havingconstants which can be obtained with available dielectrics.

To simplify this problem the term can be assumed to be small comparedwith lc so that it is possible to write 377 Zur-Wi (3) If in anyparticular problem this simplification cannot be employed, then theFormula 2 referred to :above must be used. Assuming that the simplifiedformula can be employed, then it may be required to convert the compleximpedance 2804-5100 yto a pure resistance. The modulus of this compleximpedance is 297 ohms which requires k to be 1.61 which is within therange of dielectricV constants which cannot conveniently be obtained. Toovercome this diiculty the transformer may employ two eighth wavelengthsections arranged in series as shown in Figure 7, the first section 25having a dielectric medium of dielectric constant k1 and the secondsection 26 a constant Icz. If the first section is terminated by thecomplex impedance, then the impedance seen through the two sections willbe a pure reslstance providing that where Z2 is the characteristicimpedance of one of the eighth wavelength sections and Z1 is thecharacteristic impedance of the other eighth wavelength section. It isthus possible by employing available dielectric mediums to provideeighth wavelength sections of waveguide having characteristic impedancesof the required values to satisfy the Equation 3. For instance, in theexample referred to above k1 may be equal to 4.6 giving acharacteristicimpedance Z1 of 175 ohms in which case k2 will be requiredto be 2.5 so as to afford a characteristic impedance Z2 equal to 238ohms.

Alternatively, instead of employing two eighth wavelength sections, itis possible to employ a quarter wavelength section and then an eighthwavelength section, the quarter wavelength section transforming thecomplex impedance to a suitable value to enable an available dielectricmedium to be employed for the eighth wavelength section. In this case ifZ1 is the charac teristic impedance of the quarter wavelength sectionand A-l-y'B is the complex impedance, then the impedance seen throughthe quarter wavelength section is Z12 AJ`Bl ALI-B2 The modulus of whichis:

With such an arrangement it is then necessary to make the impedance ofthe eighth wavelength section equal to this modulus. It is preferred,however, to employ two eighth wavelength sections since, in this case,the overall length of the transformer is shorter and is less susceptibleto changes in the wavelength of the transmitted energy.

If the pure resistance afforded by the section or sections of thetransformer shown in Figure or 6 is not of the required value forimpedance matching purposes, then it will be necessary as 'in thearrangements shown in Figures 2 and 3 to employ a further section oi'waveguide effectively equal to a quarter of a wavelength long to convertthe pure resistance to the required value. Thus, in some cases it may benecessary to employ one or two eighth wavelength sections in associationwith a quarter wavelength section or a one-eighth wavelength section inassociation with two sections each of a quarter of a wavelength long. Itmay even be necessary in some cases to employ two quarter wavelengthsections in series to perform the functions of the quarter wavelengthsection shown in Figures 2 and 3. This may be necessary on account ofthe fact that the dielectric constant required to give the quarterwavelength section the correct impedance is not available. If the rstquarter wavelength section has a dielectric constant k1 and the secondsection a dielectric constant of k2 and assuming that the characteristicimpedance of the guide is inversely proportional to the square root ofthe dielectric constant as assumed above, then if the resistanceproduced by the eighth wavelength section is R and that this resistanceis to be converted in order to match a guide impedance of Z0 it isnecessary to arrange that Providing the ratio of Ici to k2 satisfiesthisequation the individual values of the dielectric constants areimmaterial so that it is possible to arrange for the constants to fallwithin the available range.

If desired, instead of matchinga coaxial cable to a waveguide by meansof a probe associated with a transformer as described with reference toFigure 4 of the drawings, the necessary impedance match can be obtainedby the use of a transformer or transformers associated with thewaveguide as described with reference to Figures 6 and '7. Furthermore,it is not necessary in connection with the matching arrangement shown inFigure 4 for both transformers i6 and l'l to be associated with theprobe since, if desired, one of these transformers can be associatedwith the waveguide. y

Although in the above description certain specific lengths oftransmission lines and waveguide sections are referred to, it will beunderstood that equivalent multiple lengths can be employed.

What I claim is:

1. A wave transmission system including a wave guide, and anintercoupled coaxial cable, said guide and said cable being coupled by aprobe connected to a conductor of said cable and projecting into saidwave guide, at a fixed position along said guide, one end of said waveguide being closed, a sleeve having a length equal to one-eighth of theoperating wavelength of said system, surrounding said probe andinsulated therefrom, the characteristic impedance of the section oftransmission line formed by said sleeve and said probe being equal tothe modulus 10 of the complex impedance of said wave guide at the pointof insertion of'said probe.

2. A wave transmission system including a wave guide intercoupled with acoaxial cable the intercoupling being effected by an extension oi' thecentral conductor of said cable projecting into said wave guide at afixed position along said guide, one end of said wave guide beingclosed, a sleeve having a length equal to oneeighth of the operatingwavelength of said system surrounding said central conductor andinsulated therefrom` the characteristic impedance of the sect-ion oftransmission line formed by said sleeve and said central conductor beingequal to the modulus of the complex impedance of said wave guide at thepoint of insertion of said extension of said central conductor, and afurther one-quarter wavelength matching section interposed between saidcoaxial line and said extension of said central conductor to match theimpedance of said section of transmission line to said coaxial cable.

3. A wave transmission system including a wave guide and a coaxial cablecoupled thereto, said coupling being constituted by a probe connected toa conductor of said cable projecting into said wave guide at apredetermined position along said guide, one end of said wave guidebeing closed, the length of said probe and the predetermined positionbeing such that the two components of the wave guide impedance vary withfrequency in such a manner that the sum of the two is constant, a sleevehaving a length equal to one-eighth of the main operating wavelengthsurrounding said probe and insulated therefrom, the characteristicimpedance of the section of transmission line formed by said sleeve andsaid probe being equal to the modulus of the complex impedance of saidwave guide at the point of insertion of said probe.

4. A wave transmission system including a wave guide, and a coaxialcable coupled thereto the coupling comprising aprobe constituting anextension of the center conductor of said cable projecting into saidwave guide at a predetermined position along said guide, one end of saidWave guide being closed, the length of said probe and the predeterminedposition being such that the two components of the wave guide impedancevary with frequency in such a manner that the sum of the two isconstant, a sleeve having a length equal to one-eighth of the mainoperating wavelength surrounding said probe and insulated therefrom, thecharacteristic impedance of the section of transmission line formed bysaid sleeveand said probe being equal to the modulus of the compleximpedance of said wave guide at the point of insertion of said probe,and a further one-quarter wavelength matching section between saidcoaxial line and said probe to matchv the impedance of said section oftransmission line to the impedance of said coaxial cable.

JOHN COLLARD.

REFERENCES CITED The following references arerof record in the flle ofthis patent:

UNITED STATES PATENTS Number Name Date 2,125,597 White Aug. 2, 19382,207,690 Cork et al July 9, 1940 2,241,582 Buschbeck May 13, 19412,433,011 Zaleski Dec. 23, 1947

